A control system manipulates certain variables, referred to as “control variables,” associated with a controlled system. It does so in an attempt to cause the controlled system to achieve a particular goal, often referred to as a “set point.” A feedback control system receives information indicative of an error between the actual performance of the controlled system and the set point. It then uses this information to manipulate the control variable in an effort to reduce this error.
A common example of a control system of this type is an automotive cruise control. In such a control system, the controlled system is the automobile, the set point is the desired speed, and the control variable is the output of the throttle. In such a case, the control system measures an error signal indicative of a difference between an actual speed and the desired speed, and controls the throttle on the basis of that signal.
Other examples of control systems seek to cause a controlled system to achieve a particular state at a particular time. For example, in the transportation industry, it is desirable for trains or airplanes to reach their destination neither too early, nor too late, but on time. In principle, one could simply measure the desired distance and operate the vehicle according to some pre-determined velocity profile. However, in practice, there will be random disturbances along the route, such as traffic, or poor travel conditions. Such disturbances can be compensated for by slowing down or speeding up in response to changing conditions. Preferably, such corrections would be carried out as unobtrusively as possible.
In other cases, a vehicle may have only limited fuel available to reach a destination. In such cases, it may desirable to control fuel consumption in such a way that when the vehicle arrives at the destination at the designated time with a designated amount of residual fuel. A control system for controlling the vehicle in such an application would adaptively control fuel consumption in response to stochastic inputs. For example, different patterns of driving will result in stochastically varying fuel consumption that may need to be taken into account in deciding how to consume the remaining fuel supply.